In this study the macroscopic analysis proposed by Schapery has been applied to model the non-linear viscoelastic and viscoplastic behaviour of polyester fibres. First, a special non-contact extensometry method has been developed in order to measure the fibre response without affecting the behaviour of these extremely anisotropic fibres. An accelerated identification method has then been developed. This enables a unique and independent set of parameters to be determined, which separate the reversible and non-reversible mechanisms responsible for measured strains. The model prediction for an arbitrary loading sequence corresponds closely to the measured strains. The model has been applied here at the yarn level but can equally well be used to predict rope behaviour, either by including the identified parameters in a rope structure analysis or by identifying parameters at the rope level.